Quantitative Traits

Preliminaries

If you are already familiar with the structure of these exercises, read the Introduction first.

Note

Reminder: Save your work regularly.

Important

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Contact information

If you have questions about these exercises, please contact Dr. Kevin Middleton (middletonk@missouri.edu) or drop by Tucker 224.

Learning Objectives

The learning objectives for this exercise are:

• Explain how polygenic traits differ from Mendelian traits
• Explain how traits with continuous (also called quantitative) phenotypic measures result from the combined effects of many different genes
• Describe how many genes can each contribute a small amount to a phenotype
• Explain what quantitative trait loci (QTL) are and how QTL are discovered
• Explain how the contributions of many genes of small effect can be associated with a disease or condition

Contrasting Mendelian traits and polygenic traits

Dominant/recessive to just thinking about alternate alleles (major vs. minor)

What are quantitative traits?

Counting the ways: Binomial Coefficent

Continuous traits from combinations of many Mendelian traits

Combinations of alleles are binomial

Large numbers of small additions and subtractions are normal

Make some assumptions:

• Additivity can mean adding negative numbers
• All genes have roughly equal effect
• Gene do not interact with one another

Case study: Human height

• Best understood quantitative trait
• Yet still 700 genes

Observed variation is fixed. So adding more traits just means that each can explain a bit less of the variation while simultaneously explaining more of the variation.

NH <- readRDS("NHANES/NHANES.Rds")

The National Health and Nutrition Examination Survey (“NHANES”) began in the early 1960’s and continues to this day. The goal is to assess the health and nutrition status of a broad cross-section of the population. As part of this study, height (in cm) and body mass (in kg) are recorded for each participant.

Data from the 2017-2020 NHANES survey has data for 13137

NH |> 
  group_by(Sex) |> 
  summarize(across(.cols = everything(), list(mean = mean, sd = sd)))

# A tibble: 2 × 7
  Sex       Age_mean Age_sd Weight_mean Weight_sd Height_mean Height_sd
  <chr>        <dbl>  <dbl>       <dbl>     <dbl>       <dbl>     <dbl>
1 XX Female     36.1   24.0        66.1      29.3        152.      19.7
2 XY Male       35.9   24.5        72.6      32.1        161.      24.3

ggplot(NH, aes(Height, fill = Sex)) +
  geom_histogram(bins = 30, show.legend = FALSE) +
  scale_fill_manual(values = c("goldenrod", "firebrick")) +
  facet_grid(Sex ~ .) +
  labs(x = "Height (cm)", y = "Count")

Case study: QTL mapping

Shapiro pigeon example (dominant trait)

Threshold traits

Schizophrenia (~200 genes)

Why family history is one of the most important diagnostic tools in medicine

References